Related papers: Resolving Node Identifiability in Graph Neural Pro…
Automated reasoning and theorem proving have recently become major challenges for machine learning. In other domains, representations that are able to abstract over unimportant transformations, such as abstraction over translations and…
Machine learning on graphs is an important and ubiquitous task with applications ranging from drug design to friendship recommendation in social networks. The primary challenge in this domain is finding a way to represent, or encode, graph…
We show that on graphs with n vertices, the 2-dimensional Weisfeiler-Leman algorithm requires at most O(n^2/log(n)) iterations to reach stabilization. This in particular shows that the previously best, trivial upper bound of O(n^2) is…
Graph signal processing (GSP) is a prominent framework for analyzing signals on non-Euclidean domains. The graph Fourier transform (GFT) uses the combinatorial graph Laplacian matrix to reveal the spectral decomposition of signals in the…
Motivation: Molecular interaction networks summarize complex biological processes as graphs, whose structure is informative of biological function at multiple scales. Simultaneously, omics technologies measure the variation or activity of…
The notion of network connectivity is used to characterize the robustness and failure tolerance of networks, with high connectivity being a desirable feature. In this paper, we develop a novel approach to the problem of identifying critical…
Representational limits of message-passing graph neural networks (MP-GNNs), e.g., in terms of the Weisfeiler-Leman (WL) test for isomorphism, are well understood. Augmenting these graph models with topological features via persistent…
The $k$-dimensional Weisfeiler-Leman algorithm is a powerful tool in graph isomorphism testing. For an input graph $G$, the algorithm determines a canonical coloring of $s$-tuples of vertices of $G$ for each $s$ between 1 and $k$. We say…
Most Graph Neural Networks (GNNs) propagate messages by treating node embeddings as holistic feature vectors, implicitly assuming uniform relevance across feature dimensions. This limits their ability to selectively transmit informative…
Graph matching can be formalized as a combinatorial optimization problem, where there are corresponding relationships between pairs of nodes that can be represented as edges. This problem becomes challenging when there are potential…
Spectral graph convolutional networks are generalizations of standard convolutional networks for graph-structured data using the Laplacian operator. A common misconception is the instability of spectral filters, i.e. the impossibility to…
In this paper we present a novel graph kernel framework inspired the by the Weisfeiler-Lehman (WL) isomorphism tests. Any WL test comprises a relabelling phase of the nodes based on test-specific information extracted from the graph, for…
Graph auto-encoders are widely used to construct graph representations in Euclidean vector spaces. However, it has already been pointed out empirically that linear models on many tasks can outperform graph auto-encoders. In our work, we…
Transformers are increasingly employed for graph data, demonstrating competitive performance in diverse tasks. To incorporate graph information into these models, it is essential to enhance node and edge features with positional encodings.…
This paper develops a framework for privatizing the spectrum of the graph Laplacian of an undirected graph using differential privacy. We consider two privacy formulations. The first obfuscates the presence of edges in the graph and the…
Recently, graph neural networks have been widely used for network embedding because of their prominent performance in pairwise relationship learning. In the real world, a more natural and common situation is the coexistence of pairwise…
We show that viewing graphs as sets of node features and incorporating structural and positional information into a transformer architecture is able to outperform representations learned with classical graph neural networks (GNNs). Our…
We introduce SignNet and BasisNet -- new neural architectures that are invariant to two key symmetries displayed by eigenvectors: (i) sign flips, since if $v$ is an eigenvector then so is $-v$; and (ii) more general basis symmetries, which…
Graph neural networks can be effectively applied to find solutions for many real-world problems across widely diverse fields. The success of graph neural networks is linked to the message-passing mechanism on the graph, however, the…
Graph convolutional networks (GCNs) and its variants are designed for unsigned graphs containing only positive links. Many existing GCNs have been derived from the spectral domain analysis of signals lying over (unsigned) graphs and in each…